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  • I have a doubt, kindly clarify. - Complex numbers and quadratic equations - JEE Main-6

Which of the following is one of argument of z= -\sqrt{3}-3i

  • Option 1)

    \frac{\pi }{3}

  • Option 2)

    \frac{-5\pi }{3}

  • Option 3)

    \frac{-4\pi }{3}

  • Option 4)

    \frac{4\pi }{3}

 

Answers (1)

best_answer

\because z lies in 3rd quadrant

\therefore its principal argument =-\pi +\tan ^{-1}\left | \frac{-3}{-\sqrt{3}} \right |=-\pi +\tan^{-1}\sqrt{3}=-\pi +\frac{\pi }{3}=\frac{-2\pi }{3}

 \therefore 2n\pi-\frac{2\pi }{3} will be its general argument.

for n=1, we get argument = \frac{4\pi }{3}

\therefore  Option (D)

 

General Argument of a Complex Number -

2n\pi+\theta

- wherein

\theta is the principal argument of complex number.

 

 


Option 1)

\frac{\pi }{3}

This is incorrect

Option 2)

\frac{-5\pi }{3}

This is incorrect

Option 3)

\frac{-4\pi }{3}

This is incorrect

Option 4)

\frac{4\pi }{3}

This is correct

Posted by

Himanshu

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